בעיות נבחרות בשוקי הון: תמחור אג"ח (Fixed Income)

1. בעיות נבחרות בשוקי הון:תמחור אג"ח(Fixed Income) ד"ר כורש גליל הרצאה 7: סיכוני אשראי - מבוא

2. Introduction • Obligators might default on their obligations. • This risk is important both in asset pricing and risk management. • The price of a bond issued by one company might be different than a bond issued by other company due to the difference in credit risk. • The same fact holds also when dealing with derivatives written by two different companies (over the counter).

3. Introduction - continued Pricing • Corporate bonds bear more credit risk than treasury bonds. Risk Management • Managing credit risk is particularly important in banks and other financial institutions. Regulators specify a minimum level of capital that banks are required to keep to reflect the credit risks they are bearing.

4. The Players • 􀂄 Banks: • commercial banks, • Investment banks. • 􀂄 Borrowers: • corporates, • Sovereigns. • 􀂄 Rating agencies: • Fitch, Moody‘s, Standard & Poor‘s in the US • Maalot & Midroog in Israel. • Supervisory authorities • National authorities (e.g. SEC in US) • Basel Committee on Banking Supervision • 􀂄Investors

5. Credit Risk and the Market Failures • Adverse Selection - A borrower normally knows better its credit quality than the lender. The lenders can raise the interest rate to compensate for the expected loss, but by doing so, the only borrowers that will take loans would be the worst quality – ‘market of lemons’. • Moral Hazard – Once a loan is taken, the borrower might take risks that he wouldn’t bear if he was using his own capital. That’s due to the fact that he knows that in case of bankruptcy the lender will have to suffer the loss.

6. Dealing with the market failures • In order to deal with these market failures, the market players themselves have created tools and new techniques: • Credit rationing: financial institutions (commercial and investment banks) assign to each obligor/industry/country a limited credit. • Monitoring: Banks monitor their clients to warn them/ limit their exposure once their financial situation deteriorates. Alternatively in some cases banks find it necessary to save the client. • Certifiers: Rating agencies can verify the credit quality of a firm by using its internal information without exposing it.

7. Credit Risk? • So what do we mean when we say that firm A has a higher credit risk than firm B? • Higher probability to default within the next year? • Higher probability to default within the next 10 years? • Higher expected default loss on a particular bond (which bond?) • Higher tendency for its ‘credit quality’ to decline? (rating to be downgraded).

8. Credit Risk? - continued • Each player in the ‘credit market’ might define credit risk and measure it according to its objectives. • However, the different concepts are related: • Expected credit loss (from default) is default probability × loss given default × exposure at default.

9. Expected Loss

10. However,… • We should also pay attention to the fact that different players might have different time horizons. • We also might need a general measure for an obligor’s credit risk or alternatively for the credit risk of a single obligation. • We also should be aware of the differences between default (risk) and bankruptcy (risk) and other types of financial distress. • Indeed, a serious business…

11. Credit Risk Measurements • Credit risk’s measurement is used both in pricing and risk management. • A popular measurement is ‘Credit Rating’ that can be produced internally or externally. Normally the phrase ‘Rating’ relates to ratings provided by Rating agenciessuch as S&P and Moody’s. • However, banks normally have their own internal rating system. • In fact ratings can be also produced by usingstatistical models (Scoring models). • So we’ll first focus on credit risk measurements.

12. Measurements • n-year (mostly one-year) probability of default • Internal ratings of banks (typically) • KMV (KealhoferMcQuownVasicek, now part of Moody’s) • statistical scoring models • “Through-the-cycle” probability of default • Standard & Poor’s • Fitch • “Through-the-cycle” expected loss • Moody’s

14. Average Cumulative Default Rates (%)

15. The Rating Process • 􀂄 Rating request • 􀂄 Research • 􀂄 Management meeting • 􀂄 Rating report • 􀂄 Rating committee • 􀂄 Issuer approval / appeal possibility • 􀂄 Publication • 􀂄 Surveillance

16. Scoring Models • Altman (1968) provided a very simple model to grade firms according to their probability of default. • The score (named ‘z score’) can be calculated: • where • X1 = working capital/total assets, • X2 = retained earnings/total assets, • X3 = earnings before interest and taxes/total assets, • X4 = market value equity/book value of total liabilities, • X5 = sales/total assets

17. So… • Well, while this model is still used by some people, we should remember that it’s almost 40 years old. • Since 1968, many other models were developed in order to use better statistical methods, larger and updated databases, other relevant variables and/or to be tailored for various uses (e.g. different time horizons). • The Altman’s model teach us that everyone can produce his own internal rating/scoring model by using a simple database and simple statistical methods.

18. Merton’s Model • While there are probably thousands of Altman type models out there, there are only a few Merton type models. • Merton’s model is the first attempt to create a structural model – to put a story behind the bankruptcy/default event. • It enables both credit risk measurement and corporate bond pricing.

19. Merton Model - continued • Suppose a firm’s total value is 100$, and it has 60$ outstanding bonds. The total value is stochastic. What is the probability that the value of the firm falls beneath 60? 100 60

20. Merton’s Model • Merton’s model regards the equity as a call option on the assets of the firm. • In a simple situation the equity value is max(VT -D, 0) where VT is the value of the firm and D is the debt repayment required. • Since the price of the equity and its volatility is present in the markets, one can use it in order to find the statistical properties of V and to calculate the probability of default.

21. The KMV Implementation ofMerton’s Model

22. Conclusions • We have presented several important measurement concept concerning credit risk – PD, LGD, EL. • We have shown several common measures of credit risk – ratings, scores, market-measures. • In our next meeting we will talk about credit spread pricing. We will show how some of these measures can help us in pricing of corporate bonds.